Question

For a first order reaction : 2A(g) → 2B(g) + C(g),
the initial pressure is P, and after time t, total
pressure of reaction mixture becomes P. The rate
constant is :-​

Answer 1

• The rate constant of the reaction is 2.303/t log P₀/3P₀-2Pt.

Given-

Initial pressure is P₀.

Total pressure of reaction mixture is Pt.

Reaction is -

                          2A (g) →     2B (g)    +    C (g)

At time t=0         P₀ atm        0 atm         0 atm

At time t = t     (P₀ - 2x) atm   2x atm       x atm

Total pressure is equals to sum of all the pressures. So,

Pt = Pa + Pb + Pc

Pt = P₀ - 2x + 2x + x

Pt = P₀ + x

x = Pt - P₀

Pa = P₀ - 2x

Pa = P₀ - 2 (Pt - P₀)

Pa = 3 P₀ - 2 Pt

And we know that rate constant k = 2.303 /t log Pi/Pa, where Pi is the initial pressure and t is the time.

By putting the values we get -

k = 2.303/t log P₀/3P₀-2Pt.

Regards